Solve log_3 x + log_3 (x - 18) = 5 for x.
Answer and explanation
Correct answer: C. 27
- Step 1: Combine the logarithms: log_3 [x(x - 18)] = 5, so x(x - 18) = 3^5 = 243. Step 2. x^2 - 18 x - 243 = 0, which factorises as (x - 27)(x + 9) = 0. Step 3. The root x = -9 is rejected because it makes the logarithm undefined, so x = 27. Answer: 27. Why not the others: 9: That root makes x - 18 zero or negative, so the logarithm is not defined. 243: That is the value of the right-hand side, not of x. 45: That adds 18 where the factor is x - 18.
Practise more Exponential and logarithmic functions.
Free questions with an explanation for every one, and full timed CSAT Suneung mock tests.